The upstart stock trading venue featured in Michael Lewis’ book “Flash Boys: A Wall Street Revolt,” may apply to become a fully registered stock exchange sooner than planned, according to IEX Group’s chief executive.

“Flash Boys” hit the stands March 31 and unleashed a fierce debate over the fairness of the US stock market, which the book characterized as rigged in favor of high-speed traders who use their advantages to bilk the system for billions.

The book also thrust IEX, and its CEO, Brad Katsuyama, former head of electronic trading at a unit of Royal Bank of Canada, in New York, into the spotlight.

“We’ve been getting interest from corporate clients about listings and I think that definitely increases our interest in looking at becoming an exchange earlier than thought,” Katsuyama said in an interview.

He would not specify a time frame.

IEX is currently registered as an Alternative Trading System (ATS), or what is commonly called a “dark pool.”

Dark pools are more lightly regulated than public stock exchanges, allowing them to pick who gets to trade in them. Investors remain anonymous, stock orders are not displayed, and the rules can be kept secret.

IEX does not quite fit that mold. It offers all brokers access, its subscribers are listed on its website, and out of 45 active ATSs, it is the only one to make its rules public.

The company has said it planned to become an exchange once it hits 5 percent of US stock volume, which would make it more financially viable to take on the costs of the additional regulatory burden of being an exchange.

Since the release of Lewis’ book, IEX’s trade volume has doubled to as much as 24 million shares a day, or around half a percent of US stock volume. That might seem like a drop in the bucket, but it makes it bigger, on any given day, than four of the 13 public US stock exchanges.

If it were to become a stock exchange, IEX could challenge the New York Stock Exchange and Nasdaq OMX Group for corporate listings. The last exchange to attempt to do that was BATS Global Markets in May 2012, but it experienced a software problem during its market debut on its own exchange and pulled the IPO. It currently only lists exchange-traded products.

There may have been an easier route to becoming an exchange.

In “Flash Boys,” Lewis said IntercontinentalExchange Group, which bought NYSE Euronext last year for $12 billion, offered to buy IEX before it even opened, but Katsuyama turned down the offer.

ICE declined comment.

ICE chief executive officer Jeff Sprecher has been a vocal critic of the overall stock market, saying it is too complicated and rife with conflicts of interest.

Katsuyama would not comment on whether ICE had tried to buy his company. But he did say: “We’re very aligned in philosophy and I have only good things to say about Jeff.”